Abstract

Applying Artmann’s formula to a light beam in the TM state of wave polarization, we show analytically the existence of a large and negative Goos–Hänchen shift near the angle of the Brewster dip on reflection from a weakly absorbing semi-infinite medium. The shift is opposite that in the case of total internal reflection, and it can be an order of magnitude larger than a wavelength if the absorption of the reflecting medium is sufficiently weak. Examples are given, and the detectibility of the shift is discussed.

© 2002 Optical Society of America

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References

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  1. F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).
    [CrossRef]
  2. F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).
    [CrossRef]
  3. K. Artmann, Ann. Phys. 2, 87 (1948).
    [CrossRef]
  4. R. H. Renard, J. Opt. Soc. Am. 54, 1190 (1964).
    [CrossRef]
  5. H. K. V. Lotsch, J. Opt. Soc. Am. 58, 551 (1968).
    [CrossRef]
  6. H. K. V. Lotsch, Optik (Stuttgart) 32, 116 (1970).
  7. H. K. V. Lotsch, Optik (Stuttgart) 32, 189 (1970).
  8. H. K. V. Lotsch, Optik (Stuttgart) 32, 299 (1970).
  9. H. K. V. Lotsch, Optik (Stuttgart) 33, 553 (1971).
  10. B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
    [CrossRef]
  11. T. Tamir and H. L. Bertoni, J. Opt. Soc. Am. 61, 1397 (1971).
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  12. K. W. Chiu and J. J. Quinn, Am. J. Phys. 40, 1847 (1972).
    [CrossRef]
  13. J. J. Cowan and B. Anicin, J. Opt. Soc. Am. 67, 1307 (1977).
    [CrossRef]
  14. D. J. Rhodes and C. K. Carniglia, J. Opt. Soc. Am. 67, 679 (1977).
    [CrossRef]
  15. M. McGuirk and C. K. Carniglia, J. Opt. Soc. Am. 67, 103 (1977).
    [CrossRef]
  16. B. A. Anicin, R. Fazlic, and M. Kopric, J. Phys. A 11, 1657 (1978).
    [CrossRef]
  17. W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
    [CrossRef]
  18. H. M. Lai, F. C. Cheng, and W. K. Tang, J. Opt. Soc. Am. A 3, 550 (1986).
    [CrossRef]
  19. F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
    [CrossRef] [PubMed]
  20. E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
    [CrossRef] [PubMed]
  21. H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
    [CrossRef]
  22. H. M. Lai, S. W. Chan, and W. H. Wong, “Beam characteristics on reflection from absorbing media and large negative Goos–Hänchen-like shift near the Brewster dip,” submitted to Phys. Rev. E.
  23. E. Wigner, Phys. Rev. 98, 145 (1955).
    [CrossRef]
  24. C. C. Chan and T. Tamir, Opt. Lett. 10, 378 (1985).
    [CrossRef] [PubMed]
  25. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), p. 49.
  26. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985), pp. 438, 457, 511, and 564.
  27. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1991), Vol. II, p. 509.

2000 (1)

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

1993 (1)

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

1992 (1)

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

1986 (1)

1985 (1)

1982 (1)

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

1978 (1)

B. A. Anicin, R. Fazlic, and M. Kopric, J. Phys. A 11, 1657 (1978).
[CrossRef]

1977 (3)

1972 (1)

K. W. Chiu and J. J. Quinn, Am. J. Phys. 40, 1847 (1972).
[CrossRef]

1971 (3)

1970 (3)

H. K. V. Lotsch, Optik (Stuttgart) 32, 116 (1970).

H. K. V. Lotsch, Optik (Stuttgart) 32, 189 (1970).

H. K. V. Lotsch, Optik (Stuttgart) 32, 299 (1970).

1968 (1)

1964 (1)

1955 (1)

E. Wigner, Phys. Rev. 98, 145 (1955).
[CrossRef]

1949 (1)

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

1948 (1)

K. Artmann, Ann. Phys. 2, 87 (1948).
[CrossRef]

1947 (1)

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

Anicin, B.

Anicin, B. A.

B. A. Anicin, R. Fazlic, and M. Kopric, J. Phys. A 11, 1657 (1978).
[CrossRef]

Artmann, K.

K. Artmann, Ann. Phys. 2, 87 (1948).
[CrossRef]

Bertoni, H. L.

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), p. 49.

Bretenaker, F.

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Carniglia, C. K.

Chan, C. C.

Chan, S. W.

H. M. Lai, S. W. Chan, and W. H. Wong, “Beam characteristics on reflection from absorbing media and large negative Goos–Hänchen-like shift near the Brewster dip,” submitted to Phys. Rev. E.

Cheng, F. C.

Chiu, K. W.

K. W. Chiu and J. J. Quinn, Am. J. Phys. 40, 1847 (1972).
[CrossRef]

Cowan, J. J.

Dutriaux, L.

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Fazlic, R.

B. A. Anicin, R. Fazlic, and M. Kopric, J. Phys. A 11, 1657 (1978).
[CrossRef]

Giles, C. L.

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

Goos, F.

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

Horowitz, B. R.

Kopric, M.

B. A. Anicin, R. Fazlic, and M. Kopric, J. Phys. A 11, 1657 (1978).
[CrossRef]

Kwok, C. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Lai, H. M.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

H. M. Lai, F. C. Cheng, and W. K. Tang, J. Opt. Soc. Am. A 3, 550 (1986).
[CrossRef]

H. M. Lai, S. W. Chan, and W. H. Wong, “Beam characteristics on reflection from absorbing media and large negative Goos–Hänchen-like shift near the Brewster dip,” submitted to Phys. Rev. E.

Le Floch, A.

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Loo, Y. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Lotsch, H. K. V.

H. K. V. Lotsch, Optik (Stuttgart) 33, 553 (1971).

H. K. V. Lotsch, Optik (Stuttgart) 32, 116 (1970).

H. K. V. Lotsch, Optik (Stuttgart) 32, 189 (1970).

H. K. V. Lotsch, Optik (Stuttgart) 32, 299 (1970).

H. K. V. Lotsch, J. Opt. Soc. Am. 58, 551 (1968).
[CrossRef]

Marseille, A.

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

McGuirk, M.

Pfleghaar, E.

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

Quinn, J. J.

K. W. Chiu and J. J. Quinn, Am. J. Phys. 40, 1847 (1972).
[CrossRef]

Renard, R. H.

Rhodes, D. J.

Tamir, T.

Tang, W. K.

Weis, A.

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

Wigner, E.

E. Wigner, Phys. Rev. 98, 145 (1955).
[CrossRef]

Wild, W. J.

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), p. 49.

Wong, W. H.

H. M. Lai, S. W. Chan, and W. H. Wong, “Beam characteristics on reflection from absorbing media and large negative Goos–Hänchen-like shift near the Brewster dip,” submitted to Phys. Rev. E.

Xu, B. Y.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Am. J. Phys. (1)

K. W. Chiu and J. J. Quinn, Am. J. Phys. 40, 1847 (1972).
[CrossRef]

Ann. Phys. (3)

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).
[CrossRef]

F. Goos and H. Hänchen, Ann. Phys. 5, 251 (1949).
[CrossRef]

K. Artmann, Ann. Phys. 2, 87 (1948).
[CrossRef]

J. Opt. Soc. Am. (7)

J. Opt. Soc. Am. A (1)

J. Phys. A (1)

B. A. Anicin, R. Fazlic, and M. Kopric, J. Phys. A 11, 1657 (1978).
[CrossRef]

Opt. Lett. (1)

Optik (Stuttgart) (4)

H. K. V. Lotsch, Optik (Stuttgart) 32, 116 (1970).

H. K. V. Lotsch, Optik (Stuttgart) 32, 189 (1970).

H. K. V. Lotsch, Optik (Stuttgart) 32, 299 (1970).

H. K. V. Lotsch, Optik (Stuttgart) 33, 553 (1971).

Phys. Rev. (1)

E. Wigner, Phys. Rev. 98, 145 (1955).
[CrossRef]

Phys. Rev. A (1)

W. J. Wild and C. L. Giles, Phys. Rev. A 25, 2099 (1982).
[CrossRef]

Phys. Rev. E (1)

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, Phys. Rev. E 62, 7330 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

E. Pfleghaar, A. Marseille, and A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

Other (4)

H. M. Lai, S. W. Chan, and W. H. Wong, “Beam characteristics on reflection from absorbing media and large negative Goos–Hänchen-like shift near the Brewster dip,” submitted to Phys. Rev. E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), p. 49.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985), pp. 438, 457, 511, and 564.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1991), Vol. II, p. 509.

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Figures (2)

Fig. 1
Fig. 1

Negative lateral shift on reflection from a weakly absorbing medium z>0 near the Brewster dip; both the incident and the reflected beams are schematically represented by their respective beam axes. Dashed line, path of reflection usually expected from geometrical optics.

Fig. 2
Fig. 2

Negative GH shifts of a TM beam on reflection from a weakly absorbing medium of r=1.8 and i=0.36 (curve 1), =0.18 (curve 2), and =0.09 (curve 3) near the angle of Brewster dip θb=0.931 rad=53.3°. For comparison, curve a is the shift (already 10-fold magnified) in the TE case for =1.8+0.18i.

Tables (1)

Tables Icon

Table 1 Some Semiconductors with Large r and Small i/r, Together with Predicted Shifts Sb/λ and Reflectances Rba

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

S=-dϕkdθ,
r=tanθ-θt/tanθ+θt,
r= cos θ--sin2 θ1/2 cos θ+-sin2 θ1/2,
Imr=i cos θr-2 sin2 θr-sin2 θ1/2r cos θ+r-sin2 θ1/22,
Imrb=ir-1/4r2
Sb/λ=-r+1πrri
Rb=r-1216r2i2r2

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